sbmv (USM Version)

Computes a matrix-vector product with a symmetric band matrix.

Description

The sbmv routines compute a scalar-matrix-vector product and add the result to a scalar-vector product, with a symmetric band matrix. The operation is defined as

y <- alpha*A*x + beta*y

where:

  • alpha and beta are scalars,

  • A is an n-by-n symmetric matrix with k super-diagonals,

  • x and y are vectors of length n.

API

Syntax

event sbmv(queue &exec_queue,
  uplo upper_lower,
  std::int64_t n,
  std::int64_t k,
  T alpha,
  const T *a,
  std::int64_t lda,
  const T *x,
  std::int64_t incx,
  T beta,
  T *y,
  std::int64_t incy,
  const vector_class<event> &dependencies = {})

The USM version of sbmv supports the following precisions and devices.

T

Devices Supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

Input Parameters

exec_queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See Data Types for more details.

n

Number of rows and columns of A. Must be at least zero.

k

Number of super-diagonals of the matrix A. Must be at least zero.

alpha

Scaling factor for the matrix-vector product.

a

Pointer to input matrix A. The array holding input matrix A must have size at least lda*n. See ref:matrix-storage for more details.

lda

Leading dimension of matrix A. Must be at least (k + 1), and positive.

x

Pointer to input vector x. The array holding input vector x must be of size at least (1 + (n - 1)*abs(incx)). See ref:matrix-storage for more details.

incx

Stride of vector x.

beta

Scaling factor for vector y.

y

Pointer to input/output vector y. The array holding input/output vector y must be of size at least (1 + (n - 1)*abs(incy)). See ref:matrix-storage for more details.

incy

Stride of vector y.

dependencies

List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters

y

Pointer to the updated vector y.

Return Values

Output event to wait on to ensure computation is complete.